yolov8 位置损失函数公式

### YOLOv8 位置损失函数的公式 YOLOv8 的位置损失函数主要基于边界框回归任务的设计，通常使用的是 IoU 或其变体作为核心指标。具体来说，在 YOLOv8 中的位置损失函数可以表示为一种改进版的 CIoU 损失或者 DIoU 损失[^1]。 CIoU 损失的定义如下： \[ \text{CIoU} = 1 - \left(\frac{\rho^2(b, b_{gt})}{c^2} + \alpha v\right) \] 其中： - \(b\) 和 \(b_{gt}\) 分别代表预测框和真实框； - \(\rho(b, b_{gt})\) 是两个框中心点之间的欧几里得距离； - \(c\) 是覆盖这两个框的最小闭包区域的对角线长度； - \(\alpha\) 是一个比例因子，用于平衡重叠面积与宽高比一致性的影响； - \(v\) 表示宽高比一致性的度量，定义为： \[ v = \frac{4}{\pi^2} (\arctan(w_{gt}/h_{gt}) - \arctan(w/h))^2 \] 在某些实现中，为了进一步优化难易样本的学习效果，可能会引入 Focaler-IoU 方法来调整损失权重[^5]。这种技术通过对不同难度的样本分配不同的学习重点，从而改善整体检测性能。 以下是 Python 实现的一个简化版本的 CIoU 计算代码： ```python import torch def ciou_loss(preds, targets, eps=1e-7): """ Calculate the Complete Intersection over Union (CIOU) loss. Args: preds: Predicted bounding boxes with shape [N, 4], where N is number of predictions, and each box format should be [cx, cy, w, h]. targets: Ground truth bounding boxes with same shape as `preds`. eps: A small value to avoid division by zero. Returns: The CIOU loss tensor. """ # Convert center-width-height format to top-left-bottom-right corners px1y1 = preds[:, :2] - preds[:, 2:] / 2 px2y2 = preds[:, :2] + preds[:, 2:] / 2 tx1y1 = targets[:, :2] - targets[:, 2:] / 2 tx2y2 = targets[:, :2] + targets[:, 2:] / 2 # Compute intersection area inter_x1y1 = torch.max(px1y1, tx1y1) inter_x2y2 = torch.min(px2y2, tx2y2) inter_wh = (inter_x2y2 - inter_x1y1).clamp(min=0) inter_area = inter_wh[:, 0] * inter_wh[:, 1] # Compute union area pred_area = preds[:, 2] * preds[:, 3] target_area = targets[:, 2] * targets[:, 3] union_area = pred_area + target_area - inter_area + eps ious = inter_area / union_area # Compute distance between centers center_dist_sq = ((preds[:, 0] - targets[:, 0]) ** 2 + (preds[:, 1] - targets[:, 1]) ** 2) # Compute diagonal length of smallest enclosing box enclose_x1y1 = torch.min(px1y1, tx1y1) enclose_x2y2 = torch.max(px2y2, tx2y2) enclose_diagonal_sq = ((enclose_x2y2[:, 0] - enclose_x1y1[:, 0]) ** 2 + (enclose_x2y2[:, 1] - enclose_x1y1[:, 1]) ** 2 + eps) diou_term = center_dist_sq / enclose_diagonal_sq # Aspect ratio consistency term atan_pred = torch.atan(preds[:, 2] / preds[:, 3]) atan_target = torch.atan(targets[:, 2] / targets[:, 3]) aspect_ratio_consistency = 4.0 / (torch.pi ** 2) * ((atan_pred - atan_target) ** 2) alpha = aspect_ratio_consistency / (1 - ious + aspect_ratio_consistency + eps) ciou_loss_value = 1 - ious + diou_term + alpha * aspect_ratio_consistency return ciou_loss_value.mean() ```